Transplanckian axions !?

TL;DR

This paper examines quantum gravitational effects on axion models, showing that superplanckian periods are generally spoiled by instantons, but multi-axion setups can achieve larger periods without such issues, challenging the Weak Gravity Conjecture.

Contribution

It analyzes gravitational instantons' impact on axion inflation models and proposes that multi-axion theories can circumvent constraints, offering new insights into superplanckian field ranges.

Findings

Single axion superplanckian periods are destabilized by gravitational instantons.

Multi-axion models can achieve larger periods without higher harmonics.

Certain multi-axion theories evade the Weak Gravity Conjecture due to discrete symmetries.

Abstract

We discuss quantum gravitational effects in Einstein theory coupled to periodic axion scalars to analyze the viability of several proposals to achieve superplanckian axion periods (aka decay constants) and their possible application to large field inflation models. The effects we study correspond to the nucleation of euclidean gravitational instantons charged under the axion, and our results are essentially compatible with (but independent of) the Weak Gravity Conjecture, as follows: Single axion theories with superplanckian periods contain gravitational instantons inducing sizable higher harmonics in the axion potential, which spoil superplanckian inflaton field range. A similar result holds for multi-axion models with lattice alignment (like the Kim-Nilles-Peloso model). Finally, theories with $N$ axions can still achieve a moderately superplanckian periodicity (by a $\sqrt{N}$ factor) with no higher harmonics in the axion potential. The Weak Gravity Conjecture fails to hold in this case due to the absence of some instantons, which are forbidden by a discrete $\mathbf{Z}_N$ gauge symmetry. Finally we discuss the realization of these instantons as euclidean D-branes in string compactifications.